Subgroups — C₂×#63770 #10593769

Order 576.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3788	C₂	1	2	yes	maximal
2	C₂×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	#63770	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₂×#622	—	2	2	no	—
6	#3788	—	2	2	no	—
7	#3788	C₂²	1	4	yes	—
8	C₂×C₃²×C₈	C₄	1	1	yes	characteristic
9	C₂×C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
10	C₈×C₃⋊D₃	C₄	1	2	yes	—
11	C₈×C₃⋊D₃	C₂²	1	2	yes	—
12	C₂×D₃×C₈	—	6	2	no	—
13	C₂²×C₃⋊D₃	Q₈	1	1	yes	characteristic
14	C₂×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃⋊Dic₃	D₄	1	1	yes	characteristic
16	C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
18	C₄×C₃⋊D₃	Q₈	1	1	yes	characteristic
19	C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
20	#622	—	2	4	no	—
21	C₃²×C₈	C₂×C₄	1	2	yes	—
22	C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
23	C₂×#108	—	9	1	no	maximal, Sylow
24	C₂×C₄×D₃	—	6	2	no	—
25	C₂×C₃×C₈	—	2	2	no	—
26	C₂×C₃⋊C₈	—	6	2	no	—
27	D₃×C₈	—	6	4	no	—
28	D₃×C₈	—	6	4	no	—
29	C₂²×C₃²	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₃⋊D₃	—	2	2	no	—
31	C₂×C₃⋊D₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₃⋊D₃	C₂×Q₈	1	1	yes	characteristic
33	C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
34	C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
35	C₃⋊Dic₃	C₄⋊C₄	1	1	yes	characteristic
36	C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
37	C₂×M₁₆	—	9	2	no	—
38	C₂²×C₈	—	9	1	no	—
39	#108	—	9	4	no	—
40	C₂²×D₃	—	6	2	no	—
41	C₂×C₃×C₄	—	2	2	no	—
42	C₂×Dic₃	—	6	2	no	—
43	C₄×D₃	—	6	2	no	—
44	C₄×D₃	—	6	2	no	—
45	C₄×D₃	—	6	2	no	—
46	C₄×D₃	—	6	2	no	—
47	C₃×C₈	—	2	4	no	—
48	C₃⋊C₈	—	6	4	no	—
49	C₂×C₃²	#108	1	2	yes	complemented
50	C₂×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₃⋊D₃	—	2	1	no	—
52	C₃⋊D₃	—	2	1	no	—
53	C₂²×C₄	—	9	1	no	—
54	M₁₆	—	9	4	no	—
55	M₁₆	—	18	2	no	—
56	C₂×C₈	—	9	1	no	—
57	C₂×C₈	—	9	2	no	—
58	C₂×C₈	—	9	2	no	—
59	C₂×C₈	—	18	2	no	—
60	C₂×C₈	#157	1	1	yes	characteristic
61	C₂²×C₃	—	2	2	no	—
62	C₂×D₃	—	6	2	no	—
63	C₂×D₃	—	6	2	no	—
64	C₂×D₃	—	6	8	no	—
65	C₃×C₄	—	2	2	no	—
66	C₃×C₄	—	2	2	no	—
67	Dic₃	—	6	2	no	—
68	Dic₃	—	6	2	no	—
69	C₃²	C₂×#108	1	1	yes	characteristic, complemented, Sylow
70	C₂³	—	9	1	no	—
71	C₂×C₄	—	9	1	no	—
72	C₂×C₄	—	9	1	no	—
73	C₂×C₄	—	9	1	no	—
74	C₂×C₄	—	9	1	no	—
75	C₂×C₄	—	9	1	no	—
76	C₂×C₄	C₂×#157	1	1	yes	characteristic
77	C₈	—	9	2	no	—
78	C₈	—	18	4	no	—
79	C₈	C₂×#157	1	2	yes	—
80	C₂×C₃	—	2	4	no	—
81	C₂×C₃	—	2	2	no	—
82	D₃	—	6	4	no	—
83	D₃	—	6	4	no	—
84	C₂²	—	9	1	no	—
85	C₂²	—	9	1	no	—
86	C₂²	—	18	2	no	—
87	C₂²	C₄⋊#157	1	1	yes	characteristic
88	C₄	—	9	1	no	—
89	C₄	—	9	1	no	—
90	C₄	C₄⋊#157	1	1	yes	characteristic
91	C₄	C₂²×#157	1	1	yes	characteristic
92	C₃	—	2	2	no	—
93	C₂	—	18	1	no	—
94	C₂	—	18	1	no	—
95	C₂	#63770	1	2	yes	direct product factor
96	C₂	C₂×C₄⋊#157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#157
commutator	C₃²×C₄	C₂²×C₄
Frattini	C₄	C₂²×#157
Fitting	C₂×C₃²×C₈	C₄
socle	C₂²×C₃²	C₄⋊C₄
prime radical	C₂²×C₃⋊D₃	Q₈
cosocle	C₄×C₃⋊D₃	C₂³
hypercenter	C₂×C₈	#157
hypocenter	C₃²	C₂×#108
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #63770	C₂	direct (N × H)
49. C₂×C₃²	#108	semidirect
69. C₃²	C₂×#108	semidirect
95. C₂	#63770	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#3788	2
C₂×C₈×C₃⋊D₃	2
#63770	2
C₂×#108	9

Subgroups — C2×#63770 #10593769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63770 #10593769